The 100-year global warming potential (GWP) is the primary metric used to
compare the climate impacts of emissions of different greenhouse gases
(GHGs). The GWP relies on radiative forcing rather than damages, assumes
constant future concentrations, and integrates over a timescale of 100 years
without discounting; these choices lead to a metric that is transparent and
simple to calculate, but have also been criticized. In this paper, we take a
quantitative approach to evaluating the choice of time horizon, accounting
for many of these complicating factors. By calculating an equivalent GWP
timescale based on discounted damages resulting from

The global warming potential (GWP) is the primary metric used to assess the equivalency of emissions of different greenhouse gases (GHGs) for use in multi-gas policies and aggregate inventories. This primacy was established soon after its development in 1990 (Lashof and Ahuja, 1990; Rodhe, 1990) due to its early use by the WMO (1992) and UNFCCC (1995). However, despite the GWP's long history of political acceptance, the GWP has also been a source of controversy and criticism (e.g., Wigley et al., 1998; Shine et al., 2005; Allen et al., 2016; Edwards et al., 2016).

Key criticisms of the metric are wide ranging. Criticisms include the following: that radiative forcing as a measure of impact is not as relevant as temperature or damages (Shine et al., 2005); that the assumption of constant future GHG concentrations (Wuebbles et al., 1995; Reisinger et al., 2011) is unrealistic; that discounting is preferred to a constant time period of integration (Schmalensee, 1993); disagreements about the choice of time horizon in the absence of discounting (Ocko et al., 2017); that dynamic approaches would lead to a more optimal resource allocation over time (e.g., Manne and Richels, 2001, 2006); that the GWP does not account for non-climatic effects such as carbon fertilization or ozone produced by methane (Shindell, 2015); and that pulses of emissions are less relevant than streams of emissions (Alvarez et al., 2012). Unfortunately, including these complicating factors would make the metric less simple and transparent and would require reaching a consensus regarding appropriate parameter values, model choices, and other methodology issues. The simplicity of the calculation of the GWP is one of the reasons that the use of the metric is so widespread.

In this paper, we focus on the choice of time horizon in the GWP as a key
choice that can reflect decision-maker values, but for which additional clarity
regarding the implications of the time horizon could be useful. We also
investigate the extent to which the choice of time horizon can incorporate
many of the complexities of assessing the impacts described in the previous
paragraph. The 100-year time horizon of the GWP (GWP100) is the time
horizon most commonly used in many venues, for example in trading regimes
such as under the Kyoto Protocol, perhaps in part because it was the middle
value of the three time horizons (20, 100, and 500 years) analyzed in the
IPCC First Assessment Report. However, the 100-year time horizon has been
described by some as arbitrary (Rodhe, 1990). The IPCC AR5 (Myhre et al.,
2013) stated that “[t]here is no scientific argument for selecting 100 years
compared with other choices”. The WMO (1992) assessment has provided one of
the few justifications for the 100-year time horizon, stating that “the GWPs
evaluated over the 100-year period appear generally to provide a balanced
representation of the various time horizons for climate response”. Recently,
some researchers and NGOs have been promoting more emphasis on shorter time
horizons, such as 20 years, which would highlight the role of short-lived
climate forcers such as

While we argue that quantitative justifications for choosing appropriate GWP timescales are rare, as reflected by the judgment of the IPCC authors that no scientific arguments exist for selecting given timescales, there is a rich literature addressing many aspects of climate metrics. Deuber et al. (2013) present a conceptual framework for evaluating climate metrics, laying out the different choices involved in choosing the measure of impact of radiative forcing, temperature, or damages, and temporal weighting functions that can be integrative (whether discounted or time horizon based) or based on single future time points. Deuber et al. (2013) conclude that the global damage potential (GDP) could be considered a “first-best benchmark metric”, but recognize that the time-horizon-based GWP has advantages based on limiting value-based judgments to a choice of time horizon, reducing scientific uncertainty by limiting the calculations of atmospheric effects to radiative forcing, and eliminating scenario uncertainty by assuming constant background concentrations. Mallapragada and Mignone (2017) present a similar framework and also note that metrics can consider a single pulse of a stream of pulses over multiple years. Several authors have recognized that under certain simplifying assumptions, the GWP is equivalent to the integrated GTP, and therefore any timescale arguments that apply to analyses of one metric would also apply to the other (Shine et al., 2005; Sarofim, 2012).

A few papers have applied GDP-type approaches to evaluate the GWP in a manner similar to that of this paper. Boucher (2012) uses an uncertainty analysis similar to that used in this paper to estimate the GDP of methane. Boucher found that the GDP was highly sensitive to discount rate over a range of 1 % to 3 % and damage function over a range of polynomial exponents of 1.5 to 2.5 and that the median value of the GDP was very similar to the GWP100. Fuglestvedt et al. (2003) also used a GDP approach to map time horizons and damage function exponents to a discount rate using IS92a as an emission scenario. Fuglestvedt et al. (2003) found that a discount rate of 1.75 % and a damage exponent of 2 led to results equivalent to a GWP100. De Cara (2005), in an unpublished manuscript, also calculated the relationship between discount rates and time horizon, though they assumed linear damages.

An alternate approach is to evaluate metrics within the context of an
integrated assessment model (IAM). There are several examples of such an
approach. Van den Berg et al. (2015) analyze the implications of the use of
20-, 100-, and 500-year GWPs for

While this paper focuses on a cost–benefit approach, there is also a
potential need for cost–efficiency approaches, particularly in regard to
stabilization targets such as 2

This paper provides a needed quantification and analysis of the implications
of different GWP time horizons. We follow the lead of economists who have
proposed that the appropriate comparison for different options for GHG
emissions policies is between the net present discounted marginal
damages (Schmalensee, 1993; Deuber et al., 2013). However, instead of
proposing a switch to a GDP metric, we take the structure of the GWP as a
given due to the simplicity of calculation and the widespread historic
acceptance of its use. While other analysts have used similar approaches
(Fuglestvedt et al., 2003; Boucher, 2012), this paper reframes and clarifies
key issues and presents a framework for better understanding how different
timescales can be reconciled with how the future is valued. The paper focuses
on

The general approach taken in this paper is to calculate
the impact of a pulse of emissions of either

Impacts of emission pulses of

The analysis starts by calculating the climate effects of an emission pulse
of

This analysis of evaluating the radiative forcing, temperature, damages, and
discounted damages of a pulse emission can be used to calculate the
consistent GWP timescale for a given discount rate or, conversely, the
discount rates that are consistent with a given GWP timescale by comparing
the net present discounted marginal damages of

GWP timescales consistent with discount rates based on consistency
of the GWP ratio with the ratio of net present damages of

From Fig. 2, the discount rate implied by the GWP100 is 3.3 %
(interquartile range of 2.7 % to 4.1 %). The discount rate implied by
a 20-year GWP timescale is 12.6 % (interquartile range of 11.1 % to
14.6 %). The results in the figure are truncated to the year 2300 and the
calculation is truncated to the year 2500, which may matter at very low
discount rates due to the long lifetime of

There is much discussion regarding which discount rates are most appropriate for use in evaluating climate damages. Since 2003, the US government has used discount rates of 3 % and 7 % to evaluate regulatory actions, and 3 % was deemed appropriate for regulation that “primarily and directly affects private consumption” and 7 % for regulations that “alter the use of capital in the private sector” (OMB, 2003). From the current analysis, a 3 % discount rate is consistent with a GWP of 118 years (interquartile range of 84–171 years) and 7 % with a GWP of 38 years (interquartile range of 32–47 years). The OMB Circular also recognizes that there are special ethical considerations when impacts may accrue to future generations, and climate change is a prime example of an impact for which discount rates lower than 3 % could be justified. A number of researchers have advocated for time-dependent declining discount rates (Weitzman, 2001; Newell and Pizer, 2003; Gollier et al., 2008). The UK and France both already use declining discount rates in policy-making, and in both cases, the certainty equivalent discount rate drops below 3 % within 100 years and approaches 2 % within 300 years (Cropper et al., 2014).

This paper does not select a single “correct” discount rate. However, the analysis shows that the 100-year timescale is consistent, within the interquartile range, with the 3 % discount rate that is commonly used for climate change analysis. In contrast, a 20-year time horizon for the GWP implies discount rates larger than those used in any climate change analysis publications to date.

Figure 2 shows the median, interquartile, interdecile, and extremes of the
equivalent GWP time horizon corresponding to a given discount rate from a
sensitivity analysis. The uncertainty was calculated assuming equal
likelihood of each of the 972 combinations of all of the parameter choices
used in this paper: four RCPs, three climate sensitivities, three damage exponents,
three forcing imbalance options, three temperature offsets, and three GDP growth rates.
The ranges chosen for each parameter are described in the Methods section. The
parameters with the largest effect on the uncertainty of the calculated GWP
(at a discount rate of 3 %) are the rate of GDP growth and the damage
exponent (see Table 1). For these six parameters, the choices that lead to
larger damages from

Parameter sensitivity analysis: examining the sensitivity of the GWP–discount rate equivalency as shown in the uncertainty ranges in Fig. 2 as a function of the individual parameters of the calculation. The ratio is calculated as the ratio of the median of the estimated GWPs given the highest and lowest value of each parameter. The results in this table are derived assuming a discount rate of 3 %.

Optimal timescale of non-

While

In addition to investigating the sensitivity of these results to different choices of the six listed parameters and five different gases, several other sensitivity experiments were performed. These experiments were chosen to investigate whether certain assumptions are important and alternate approaches to constructing the model.

The first set of experiments involve analysis choices that end up having
little difference in terms of timescale estimation. In general, this is
because changes in these choices affect both the GWP and the damage
estimation equally and therefore cancel out. One experiment involved
changing the size of the emissions pulse to 373 MMT (about 1 year of
anthropogenic emissions according to Saunois et al., 2016). The effect on
damage ratios of this change was less than 1 %. Another experiment
involved doubling the radiative efficiency of methane; while this led to a
doubling of the estimated damage ratio, it also led to a doubling of the
estimated GWP such that the change in estimated timescale was about

Another experiment considered the use of a Ramsey-type framework for discounting future damages. The use of such a framework has been recommended by the National Academies (NAS, 2017). In this framework, discount rates are a function of the marginal utility of consumption, the pure rate of time preference, and the future growth rate of per capita consumption. It is the latter dependence that makes this sensitivity analysis particularly interesting, as this pairs higher consumption growth (leading to higher damage ratios) with higher discount rates (leading to lower damage ratios). For this experiment, the Ramsey parameters were calibrated to yield an average discount rate for the reference GDP of 5 % over the first 30 years of the analysis given a pure rate of time preference of 0.01 %. Under this assumption, the median timescale under the reference GDP scenario increases to 135 years because even though the initial discount rates are higher than 3 %, over the entire period of the analysis the average discount rate is only 1.5 %. However, unlike in the original analysis, under the high GDP growth scenario the damage ratio increases and the equivalent timescale decreases to 90 years because the increase in discount rate resulting from high growth has a larger effect on damages than the long-term increase in GDP (and vice versa for low GDP growth). The difference between the damage ratios for the high and low GDP growth scenarios is still about a factor of 2. A future analysis could pair GDP scenarios with emissions scenarios to take into account the potential correlation of the two.

Boucher (2012) and Fuglestvedt et al. (2003) both applied similar approaches to the one used in this paper, but both papers identified a discount rate consistent with the GWP100 that was somewhat lower than the median 3.3 % value found in this paper. The most evident difference between the approach in these previous papers and this article is that this article assumes that damages are expressed as a percent of GDP, and the previous analyses did not. In order to more closely emulate the Boucher and Fuglestvedt approach, the model was tested by using constant GDP over the entire time period, and the GWP100 was found to be the most consistent with a discount rate of 1.2 % (interquartile range of 1.0 % to 1.9 %) in contrast to 3.3 % (interquartile range of 2.7 % to 4.1 %).

Myhre et al. (2013) justified the exclusion of the 500-year GWP based on the
large uncertainties and ambiguities involved with far future projections.
This analysis extends through 2500 and therefore might be subject to some of
those same uncertainties. Therefore, the effect of two shorter time periods
was investigated. When truncating the analysis after 150 years, the GWP100
was still found to be consistent with a discount rate of 3.3 %, with the
upper interquartile bound also remaining constant at 4.1 %, though the
lower end of the interquartile range decreased modestly to 2.4 %. When
the analysis was truncated at 100 years into the future, the implicit
discount rates dropped more substantially, to 2.6 % (interquartile range
of 1.5 % to 3.5 %). Truncating the analysis will naturally make

A final experiment considered the inclusion of damages due to rate of change
and due to absolute temperature. The inclusion of rate-of-change damages
has had important influences on previous analyses. For example, in Manne and
Richels (2001), the dynamic optimization solution for approaching a
temperature threshold placed little value on

There are a number of uncertainties involved in this analysis. They can be
divided into three categories: those that may change the relative
climate-related discounted damages of

As shown above, uncertainties in this analysis that do not have a large
impact on the calculated GWP timescale include factors that have similar
effects on the GWP and the

In contrast, the timescale of ocean heat uptake, the lag between the timing of atmospheric temperature response to forcing and the response of sea level (e.g., Zickfeld et al., 2017), and other issues that are inherent to the timing of climate impacts – but are not necessarily included in the GWP calculation – might all affect the implied timescale. One potential way to explore some of these effects would be to use a more complex climate model to evaluate the radiative forcing and temperature effects of the emission pulses. The shape of the damage function can also have a substantial effect; different exponents for the polynomial form were tested, as was the inclusion of rate of change, but the full range of possible damage functions is substantially larger, including multi-polynomial behavior (Weitzman, 2001) and the potential for persistent influences on economic growth (Burke et al., 2015).

An additional category of effects has less relevance to an analysis of
an appropriate timescale for climate impacts, but would be important for overall
valuation. These are generally gas-specific effects that should most
appropriately be considered on a case-by-case basis rather than folding into
a timescale analysis that will influence the mitigation choices for all
gases. One example is the inclusion of

The analysis presented here suggests that the use of a 100-year time horizon
for the GWP is in good agreement with what many consider an appropriate
discount rate; however, we offer several caveats. Most importantly, this
analysis makes the assumption that the net present damage of

This metric approach is also not designed to achieve a long-term temperature
goal such as stabilization at 2

This analysis uses a global damage potential approach to calculate the implicit discount rate corresponding to different GWP timescales. While this is not the first analysis to calculate the implicit discount rate of the 100-year GWP (Boucher, 2012; Fuglestvedt et al., 2003), the framework presented here allows for a more complete and wide-ranging analysis of sensitivities than has been presented previously, and the connection between the timescale and the implicit discount rate is made more clearly. The 100-year GWP is the inter-gas comparison metric with the widest use, and the results presented here show that the 100-year timescale is consistent with an implied discount rate of 3.3 % (interquartile range of 2.7 % to 4.1 %). Alternatively, the 3 % discount rate used for calculating social damages in some regulatory impact analysis contexts is consistent with timescales of 84–171 years. The uncertainty range in the results is the most sensitive to assumptions regarding future GDP growth and to the choice of exponent in the damage function. These results are insensitive to assumptions regarding radiative efficiency, pulse size, and consistent treatment of climate–carbon feedbacks. At discount rates of 3 % or higher, the analysis can be truncated to 150 years (rather than the default calculation through 2500) with little effect. The inclusion of damages resulting from the rate of change in addition to absolute temperature changes has little effect except in the case of a low-emissions future, for which it results in a decrease in the timescale consistent with a 3 % discount rate to 54 years. Applying the methodology in this paper to calculate the implied intertemporal values of a 20-year GWP, a timescale that has received some recent attention, results in an implicit discount rate of 12.6 % (interquartile range of 11.1 % to 14.6 %).

These results provide support for the contention that 100 years is a
reasonable timescale choice for the GWP given the assumption that the
relative climate damage of pulses of different greenhouse gases is an
appropriate means of valuation and that the 3 % discount rate is a
reasonable measure of the value of the future. This finding is robust to a
number of sensitivity analyses. In contrast, the analysis suggests that the
20-year GWP timescale is the most consistent with an implicit discount rate much
higher than the standard social discount rate, except in scenarios with low
future emissions and high rate-of-change damages, similar to concerns
expressed in other analyses (Shoemaker and Schrag, 2013). However, while the
implicit timescale was derived from analyzing the climate impacts resulting
from

The methodology presented here is transparent (the code is available in the Supplement), rigorous (the parameters and functional forms are derived from respected sources), and flexible (as demonstrated by a wide range of sensitivity analyses from the inclusion of rate-of-change damages to Ramsey discounting). This framework can be a valuable resource for quantitatively examining appropriate timescales given different assumptions about discounting, the relationship of damages to both absolute and rate of temperature changes, tipping points, future emissions scenarios, and other factors.

The R code used in developing this paper can be found in the Supplement.

Both MCS and MRG contributed to experiment design, coding, figure development, and paper writing.

The authors declare that they have no conflict of interest.

This publication was developed under assistance agreement no. X3-83588701 awarded by the U.S. Environmental Protection Agency to AAAS. It has not been formally reviewed by the EPA. The views expressed in this document are solely those of the authors and do not necessarily reflect those of the agency. The EPA does not endorse any products or commercial services mentioned in this publication.

Michael R. Giordano was supported as a Science and Technology Policy Fellow by the American Association for the Advancement of Science (AAAS) STPF program. The authors would like to thank numerous colleagues at the EPA for their thoughts and discussions regarding GHG metrics and climate economics. Edited by: Daniel Kirk-Davidoff Reviewed by: William Collins and three anonymous referees